Gimam

ADDITIONAL EXERCISES

QUESTION 1

The single line diagram of a 3 bus system is shown in Figure Q1. Using Fast Decoupled loadflow method, determine the voltage and angle for bus 2 and bus 3 up to first iteration only. (20 marks)

MVAbase = 100 MVA
BUS 2
BUS 2

Z23 = 0.1 + j0.3 p.u
Z23 = 0.1 + j0.3 p.u
BUS 3
BUS 3

V2=1.05 p.u
V2=1.05 p.u

PL3 = 300 MW
QL3 = 200 MVar
PL3 = 300 MW
QL3 = 200 MVar

Z12 = 0.1 + j0.5 p.u
Z12 = 0.1 + j0.5 p.u
Z13 = 0.2 + j0.4 p.u
Z13 = 0.2 + j0.4 p.u

BUS 1
(slack)
BUS 1
(slack)

PL1 = 250 MW
QL1 = 300 MVar
PL1 = 250 MW
QL1 = 300 MVar

V1 = 1.0 p.u
V1 = 1.0 p.u

Figure Q1

QUESTION 2

A system with three generating units is supplying a load of 1000 MW. The cost function in $/hr for the units are:-

C1 = 300 + 7.2 P1 + 0.045 P12
C2 = 275 + 5.4 P2 + 0.085 P22
C3 = 350 + 6.7 P3 + 0.055 P32
The generation limits for the units are given as: 150 MW P1 650 MW 100 MW P2 450 MW 70 MW P3 350 MW.

a) neglecting the system losses, find the optimal dispatch for each generator and the total generation cost in $/hr. (12 marks)

b) Due to a substation failure, the demand was reduced to 800 MW, determine the new optimal dispatch for the system if generating unit 3 is on forced outage. (8 marks) c) Discuss what are the actions need to be taken in order to reduce the losses in the system. (6 marks)

QUESTION 3

a) Three generating units are operating in parallel at 50 Hz and supplying electrical energy to an area A. The speed droop characteristics, ratings and generated output for each unit are given as follows:- Generator 1: R1u = 3 %, SR1 = 650 MW Pg1 = 450 MW
2: R2u = 2.5 %, SR2 = 500 MW Pg2 = 300 MW
3: R3u = 6 %, SR3 = 400 MW Pg3 = 250 MW If the total load increased by 100 MW, determine the new power to